the thing with CEXs is that they track (and they are supposed to track) every transaction their users make. So, if you deposit $500 three times and immediately buy and withdraw the XMR to your self-custody, the CEX will know the following:
(a) Trêvoid deposited $1500
(b) Trêvoid bought 2 XMR, then 2.1 XMR and then 1.9 XMR with this money, leaving them with a total of 6 XMR and $0.
(c) Trêvoid withdrew 1.5 XMR to address XYZ, then 2.5 XMR to address OPK and then 2 XMR to address UJM.
Centralized exchanges are basically like banks, but (at least for the moment) less strictly regulated, and I assume they'd actually share more data with more different governments than banks do.
For both, it's safe to assume they keep all records of all transactions forever.
If I go to an ATM 3 times, and take out €500 3 times, all the bank knows is that Marcel now has €1500 in his pocket. If I were to deposit that again, they can assume it's the same
amountpile of bills or
a different
amountbills. But if someone else deposits €1500, they have no idea if there's a link between the transactions. XMR is more or less the same.